Block #92,895

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 8/2/2013, 12:55:24 AM · Difficulty 9.2014 · 6,716,440 confirmations

TWN

Bi-Twin Chain

Interleaved pairs of primes that differ by 2, forming twin prime pairs at each level.

Block Header

Block Hash

548a6ebed0b6e01d54e0d68366cb5f02f190387ff6ef43a73848989eba202e97

View on Chainz ↗

Height

#92,895

Difficulty

9.201426

Transactions

Size

431 B

Version

Bits

093390ad

Nonce

447,997

Timestamp

8/2/2013, 12:55:24 AM

Confirmations

6,716,440

Mined by

⛏️ P2SHAFuCxcocotT3P65GNe7WxirDpmZi6Xm9qe

Merkle Root

14a53f472b6da2af36f98493f44896646369cf0ccaefdbba2b73b9c032f98bb3

Transactions (2)

Coinbasee15d6d74fcc7db…c66b4f1f739883

1 in → 1 out11.8000 XPM109 B

AFuCxcoc…Zi6Xm9qe

5f127edb00bd8d…c31525fe3fb5db

1 in → 2 out1.9951 XPM227 B

Af61zvbi…aERQ1am1 AM4DUx4F…6EcjKqgF

Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) — it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

7.513 × 10¹⁰⁶(107-digit number)

75137267980615350203…88204037629255682219

Discovered Prime Numbers

Lower: 2^k × origin − 1 | Upper: 2^k × origin + 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

Level 0 — Twin Prime Pair (origin ± 1)

origin − 1

7.513 × 10¹⁰⁶(107-digit number)

75137267980615350203…88204037629255682219

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.513 × 10¹⁰⁶(107-digit number)

75137267980615350203…88204037629255682221

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: origin + 1 − origin − 1 = 2 (twin primes ✓)

Level 1 — Twin Prime Pair (2^1 × origin ± 1)

2^1 × origin − 1

1.502 × 10¹⁰⁷(108-digit number)

15027453596123070040…76408075258511364439

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.502 × 10¹⁰⁷(108-digit number)

15027453596123070040…76408075258511364441

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^1 × origin + 1 − 2^1 × origin − 1 = 2 (twin primes ✓)

Level 2 — Twin Prime Pair (2^2 × origin ± 1)

2^2 × origin − 1

3.005 × 10¹⁰⁷(108-digit number)

30054907192246140081…52816150517022728879

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.005 × 10¹⁰⁷(108-digit number)

30054907192246140081…52816150517022728881

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^2 × origin + 1 − 2^2 × origin − 1 = 2 (twin primes ✓)

Level 3 — Twin Prime Pair (2^3 × origin ± 1)

2^3 × origin − 1

6.010 × 10¹⁰⁷(108-digit number)

60109814384492280162…05632301034045457759

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.010 × 10¹⁰⁷(108-digit number)

60109814384492280162…05632301034045457761

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^3 × origin + 1 − 2^3 × origin − 1 = 2 (twin primes ✓)

Level 4 — Twin Prime Pair (2^4 × origin ± 1)

2^4 × origin − 1

1.202 × 10¹⁰⁸(109-digit number)

12021962876898456032…11264602068090915519

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 consecutive prime numbers forming a Bi-Twin Chain. The prime chain origin — the large number shown above — anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

★☆☆☆☆

Rarity

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 × 3 × 5 × 7 × …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial — that divisibility is part of the proof.

Prime Chain Origin = First Prime × Primorial (2·3·5·7·11·…)

Source: Primecoin prime.cpp — CheckPrimeProofOfWork()

This is why the origin has many small prime factors — those factors are the primorial divisor. The chain then extends from the first prime using the TWN formula:

TWN: twin pairs (p, p+2) where p = origin/primorial − 1 and p+2 = origin/primorial + 1

Cross-reference on Chainz Explorer

Block #92,895

Cookie Preferences